Spatial locality brings the advantages of computation speed-up and sequence reuse to molecular computing. In particular, molecular walkers that undergo localized re- actions are of interest for implementing logic computations at the nanoscale. We use molecular spider walkers to implement logic circuits. We develop an extended multi- spider model with a dynamic environment wherein signal transmission is triggered via localized reactions, and use this model to implement three basic gates (AND, OR, and NOT) and a cascading mechanism. We develop an algorithm to automatically generate the layout of the circuit. We use a kinetic Monte Carlo algorithm to simulate circuit computations, and we analyze circuit complexity: our design scales linearly with formula size and has a logarithmic time complexity.